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      03-16-2009, 08:24 PM   #1
ktdw
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Question for a math wiz

It's been too long since calculus, and I need a formula to calculate the distance traveled based a rate of acceleration.

For example, lets assume I'm going at a constant 65 mph , and a car was going to catch me from a dig. At a rate of acceleration of (let's assume it's a Ford Crown Victoria), what is distance that he would be required to travel?

Bonus: What is the distance if his top speed was capped at a 100mph or so?


Sorry, if this should be in different forum, but I'm sure somebody here knows what I'm talking about.
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      03-16-2009, 08:38 PM   #2
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x = x0 + v0*t + 0.5*a*t^2

Where
x = Distance [ft]
x0 = Distance at the Start [ft]
v0 = Initial Velocity [ft/sec]
a = Rate of Acceleration [ft/sec^2]
t = elapsed time [sec]
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      03-16-2009, 08:40 PM   #3
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I've used this page before... http://www.ajdesigner.com/constantac...avelocitya.php

it can calculate the following:

Velocity
velocity
acceleration
time
initial velocity

Average Velocity
average velocity
initial velocity
velocity

Displacement
distance or displacement
time
average velocity
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      03-16-2009, 08:51 PM   #4
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I used to have a crown victoria with the police package and they top out at 108-112, FYI
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      03-16-2009, 08:53 PM   #5
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wait, your post doesnt mention the rate of acceleration of the ford
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      03-16-2009, 11:53 PM   #6
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simple answer

lights off, hit the gas, take the first exit
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      03-17-2009, 12:51 AM   #7
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Soon as you mentioned the Crown Vic, the first thing I thought about was how long the police car would take to catch you!
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      03-17-2009, 12:58 AM   #8
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what if its in NJ? the cops have charger r/ts here
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      03-17-2009, 01:12 AM   #9
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Assuming his 0 to 60 is 6 seconds which i think is fair, he would take 1 second per 10 mph.

A total of 65 mph means his avg speed would be around ~30 for the duration of the acceleration assuming it was linear. That means he would be going 6 seconds x 30 mph = 6 sec x 30 mph / 60 mins per hour / 60 secs per min x 5280 feet per mile = 44 feet x 6 sec = 264 feet

Over those 6 seconds you would have gone roughly double that so you would be at 528 feet. Assuming he continued gunning it he would get to 105 mph in about 6 more seconds and you two would be at the same position because you would have gotten another 528 feet in those 6 seconds but he would have gained all the rest he needed.

Long story short i figure he would have caught up to you in about 12 seconds after having started to accelerate. If you add in factors such as getting back in the car, braking when he pulls up to you, other cars. etcc you have at max 20 seconds before he is on your ass or he could be there in as little as 13 seconds.

Total distance would be ~1000 to ~1200 feet from the cops position or about a 1/5 of a mile.

This is all based on the assumptions i made of course and i might have messed up the math but it seems good to me. The biggest problem is most likely the crown vics acceleration because I know it is not linear and near the top end it is much slower so you have to take that into account.
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      03-17-2009, 01:42 AM   #10
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If you're going 120+ you going to jail anyways.. Might as well take a chance...If you go 140+ He'll probably let you go die.. LOL
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      03-17-2009, 08:41 AM   #11
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usc has got the general equation right, except that it assumes that your acceleration is at a constant rate. You would actually need to integrate acceleration with respect to distance to 100% accurate, but the equation usc gave would be the best approximation.

As for knowing the max speed and wanting distance:

Vmax^2 - Vinitial^2 (0 is starting from a stop) = 2*acceleration*distance

or rearranged:

(Vmax^2)/(2*acceleration)
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      03-17-2009, 08:20 PM   #12
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If you're going where I think you are, the speed of electromagnetic propagation in our atmosphere (roughly c) and the acceleration and delays involved in approaches from other relative positions than behind you (e.g., entering at the next intersection or on-ramp) must be considered.

You can surely beat many vehicles, but the instant said vehicles have the opportunity, every similarly tasked vehicle within miles will be converging on your projected location.

Do you ever notice all the little flower clusters along the highway and roads, the little 'drive safely' signs with a flower collection?

These are signals to be careful and are at least part of the reason going 100+ is seriously illegal on our roads.

Not to nag, but enjoy your car, safely. It's not worth the lives it could cost. If you feel the need for super speeds, find a track.
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      03-18-2009, 01:02 PM   #13
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are you planning on pissing off a trooper in the immediate future?
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      03-18-2009, 08:44 PM   #14
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Quote:
Originally Posted by Jet335i View Post
are you planning on pissing off a trooper in the immediate future?
Wasn't planning on it I'm writing a declaration to contest a speeding ticket I recieved. No radar was used, so it's pretty much based on the trooper's estimation of my speed.
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      03-19-2009, 12:42 AM   #15
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I think the real question should be, what is the mathematical possibility of me outrunning a cop in my car

Getting away from the po po in a sport car...maybe 10%

Buy a bike if you want to run
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      03-19-2009, 01:05 AM   #16
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Sure you can run for a while, but the roads are not endless.
Living in NY... even if I owned a Veyron, I would think twice before trying to outrun cops.
I would beat them on the open roads, but you have to account for traffic, turns, red lights, intersections, etc.

If you are running and plan on taking the next exit, well you will have to slow down for that exit. When you slow down, the distance between you and the cop will decrease enormously, which will give the cop a chance yo see your plate or gain on you since it is a lot easier to follow then to invent your own route.

If it is a wide open road and you are doing 100mph+ and the cop is stopped, then run and keep it above 130mph for a while before you take the next exit.
This is unrealistic though since there will be traffic on the road, or turns that will force you to slow down if you value your life (never mind other peoples lives).


PS. Dont listen to those that say "you are already fvcked if you are doing 120mph"... because you will be fvcked 10 times worse if you try and outrun a cop.

PS2. If you are going to run, be at least 90% sure you will get away unless something happens such as a flat tire or your car goes into limp mode on you.
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      03-19-2009, 01:41 AM   #17
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What's funny is that is was kinda dark when I got pulled over, and I couldn't even see the lights on the roof. I was cruizing just a tad faster than traffic, 80ish, and I saw headlights coming up on me. I almost gunned it, but paused when I noticed that the headlights were rectangular. Thank god for that though...I could've easily turned that $300 ticket into jail time
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      03-21-2009, 01:17 AM   #18
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lol a limp mode huh?

imagine trying to run from the cops and seeing a half engine light

that would be something

emailing terry from the back of the police car and shit
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      03-21-2009, 05:03 AM   #19
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Quote:
Originally Posted by ktdw View Post
What's funny is that is was kinda dark when I got pulled over, and I couldn't even see the lights on the roof. I was cruizing just a tad faster than traffic, 80ish, and I saw headlights coming up on me. I almost gunned it, but paused when I noticed that the headlights were rectangular. Thank god for that though...I could've easily turned that $300 ticket into jail time
Yeah man, cops often drive like dicks, I've almost tried to race when they came up on me so many times lol. Luckily I play very fair or even handicap myself when someone trys a flyby race to further prove my dominance which is when i shit myself and realize it was a cop and act normal... Not much longer though, might join the force this year, weird to hear right, weirder to say
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      03-21-2009, 05:48 AM   #20
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Quote:
Originally Posted by ktdw View Post
Wasn't planning on it I'm writing a declaration to contest a speeding ticket I recieved. No radar was used, so it's pretty much based on the trooper's estimation of my speed.

I suggest a lawyer

Make sure your argument is a legal one, not one that accuses the cop estimation as faulty simply based on your math.

A judge could care less about what you think about the cop but if you present her with the laws that state the cop needs to have some sort of measurement on you, then you will win.

Legally a case based on a visual estimation should be very easy to win for you. If he paced you though then it will be much harder.
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      03-21-2009, 06:16 AM   #21
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Quote:
Originally Posted by T2x View Post
Assuming his 0 to 60 is 6 seconds which i think is fair, he would take 1 second per 10 mph.

A total of 65 mph means his avg speed would be around ~30 for the duration of the acceleration assuming it was linear. That means he would be going 6 seconds x 30 mph = 6 sec x 30 mph / 60 mins per hour / 60 secs per min x 5280 feet per mile = 44 feet x 6 sec = 264 feet

Over those 6 seconds you would have gone roughly double that so you would be at 528 feet. Assuming he continued gunning it he would get to 105 mph in about 6 more seconds and you two would be at the same position because you would have gotten another 528 feet in those 6 seconds but he would have gained all the rest he needed.

Long story short i figure he would have caught up to you in about 12 seconds after having started to accelerate. If you add in factors such as getting back in the car, braking when he pulls up to you, other cars. etcc you have at max 20 seconds before he is on your ass or he could be there in as little as 13 seconds.

Total distance would be ~1000 to ~1200 feet from the cops position or about a 1/5 of a mile.

This is all based on the assumptions i made of course and i might have messed up the math but it seems good to me. The biggest problem is most likely the crown vics acceleration because I know it is not linear and near the top end it is much slower so you have to take that into account.

I have test a real police car (with all stock in trunk) with my g-tech:

crown vict 2007 v8 4.6 : 0-60mph = 8.55
impala 2007 v6 : 0-60 = 7.94

A+
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      03-21-2009, 07:48 AM   #22
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Quote:
Originally Posted by BobVader View Post
I have test a real police car (with all stock in trunk) with my g-tech:

crown vict 2007 v8 4.6 : 0-60mph = 8.55
impala 2007 v6 : 0-60 = 7.94

A+
wow i never thought a cops car could be that slow hahahaha
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